isolate and solve the variable in this eqaution, make sure to explain the procces
4(3x-2)=-24
To isolate and solve for the variable in the equation 4(3x-2)=-24, we can follow these steps:
1. Start by distributing the 4 to both terms within the parentheses:
4 * 3x = 12x
4 * -2 = -8
2. Rewrite the equation with the distributed terms:
12x - 8 = -24
3. Next, we want to get the term with the variable (12x) on one side of the equation and the constant terms (-8 and -24) on the other side. To do this, we'll perform algebraic operations to isolate the variable.
a. Begin by adding 8 to both sides of the equation:
12x - 8 + 8 = -24 + 8
12x = -16
b. Now, we divide both sides of the equation by 12 to solve for x:
(12x)/12 = (-16)/12
x = -16/12
Simplifying the right side:
x = -4/3
4. Therefore, the solution to the equation 4(3x-2)=-24 is x = -4/3.
To double-check our solution:
Substitute x = -4/3 back into the original equation:
4(3(-4/3)-2) = -24
4(-4 - 2) = -24
4(-6) = -24
-24 = -24
The equation holds true with x = -4/3, confirming our solution.
To isolate and solve the variable in the equation 4(3x-2) = -24, we will follow several steps. Let's go through the process step-by-step:
Step 1: Distribute the 4 to the terms inside the parentheses:
4 * 3x - 4 * 2 = -24
12x - 8 = -24
Step 2: Move the constant term to the other side of the equation by adding 8 to both sides:
12x - 8 + 8 = -24 + 8
This simplifies to:
12x = -16
Step 3: Divide both sides of the equation by 12 to solve for x:
12x / 12 = -16 / 12
Simplifying further:
x = -4/3
Therefore, the solution to the equation is x = -4/3.
To isolate and solve the variable in the equation 4(3x - 2) = -24, we will follow these steps:
Step 1: Distribute the 4 to the terms inside the parentheses:
12x - 8 = -24
Step 2: Add 8 to both sides of the equation to get rid of the -8 on the left side:
12x - 8 + 8 = -24 + 8
12x = -16
Step 3: Divide both sides of the equation by 12 to solve for x:
12x/12 = -16/12
x = -4/3
Therefore, the solution to the equation is x = -4/3.